Some of the people who disliked or distrusted Lockhart:
- Hagrid (admittedly not a teacher in book 2)
- and probably most of the other staff
From Pottermore (emphasis mine):
Many staff were baffled as to the reason that Albus Dumbledore chose to invite Gilderoy Lockhart back to Hogwarts as Defence Against the Dark Arts teacher. While it was true that it had become almost impossible to persuade anybody else to take the job (the rumour that it was cursed was gathering strength both inside and outside Hogwarts), many teachers remembered Lockhart as thoroughly obnoxious, whatever his later achievements.
Albus Dumbledore’s plans, however, ran deep. He happened to have known two of the wizards for whose life’s work Gilderoy Lockhart had taken credit, and was one of the only people in the world who thought he knew what Lockhart was up to. Dumbledore was convinced that Lockhart needed only to be put back into an ordinary school setting to be revealed as a charlatan and a fraud. Professor McGonagall, who had never liked Lockhart, asked Dumbledore what he thought students would learn from such a vain, celebrity-hungry man. Dumbledore replied that ‘there is plenty to be learned even from a bad teacher: what not to do, how not to be’.
That quote gives us "many staff", Dumbledore (dislike not specifically mentioned, but at least distrust and suspicion of what Lockhart truly was), and McGonagall. It's also likely that several of the teachers had also been teachers back in Lockhart's day, and would remember his schoolboy exploits, which included (again from Pottermore):
Lockhart told anyone who would listen that he would succeed in making a Philosopher’s Stone before leaving school and that he intended to captain England’s Quidditch team to World Cup glory, before knuckling down to becoming Britain’s youngest Minister for Magic.
If he was not first and best, he would rather not participate at all. Increasingly, he directed his talents towards short cuts and dodges. He valued learning not for its own sake, but for the attention it brought him. He craved prizes and awards. He lobbied the Headmaster to start a school newsletter, because he liked nothing better than to see his name and photograph in print.
Never very popular, he nevertheless achieved his primary goal of school-wide recognition through repeated, attention-getting exploits. He received a week’s worth of detentions for magically carving his signature in twenty-foot-long letters into the Quidditch pitch. He managed to create a massive, illuminated projection of his own face, which he would send skywards in imitation of the Dark Mark. He sent himself eight hundred Valentine’s cards one year, which caused such a pile-up of owls in the Great Hall that breakfast had to be abandoned (far too many feathers and droppings in the porridge).
When Lockhart finally left Hogwarts, it was to a faint sigh of relief from the staff.
From HP and the Chamber of Secrets (book, emphasis mine):
"Like I don' know. An' bangin' on about some Banshee he banished. If one word of it was true, I'll eat my kettle. [...] I told Lockhart yeh didn' need teh. Yer more famous than him without tryin'."
"Bet he didn't like that," said Harry, sitting up and rubbing his chin.
"Don' think he did," said Hagrid, his eyes twinkling. "An' then I told him I'd never read one o' his books an' he decided ter go."
So Hagrid was willing to go as far as to criticise him to his face.
And from the film adaptation of HP and the Chamber of Secrets:
Severus Snape: "A girl has been snatched by the monster, Lockhart. Your moment has come at last."
Lockhart: "My moment?"
Severus Snape [sneeringly]: "Weren't you saying just last night that you've known all along where the entrance to the Chamber of Secrets is?"
So we can add Snape to the list of those who were openly critical of Lockhart to his face.